383 is an interesting prime. It's palindromic prime, which is sum of the first 3-digit palindromic primes (101 + 131 + 151). It's also a prime number that can be get summing up a number \(n\) with a same reversed number, where the \(n\) is in this case equal to 241 (241 is also prime) (So it's 241 + 142).

A method for generating a sequence of primes is to start with 1, then choosing the smallest prime successor of a multiple of the previous number in each step. The compositeness can be easily certified by Fermat or Miller-Rabin, and the primality by Pratt. The resulting sequence starts with 1, 2, 3, 7, 29, 59, 709, … (OEIS A061092).

719 is a prime number. As 119, 121 and 721 are all composite, it is the only 3-digit factorial prime.

By fitting the least-degree polynomial to the first n odd primes, one can attempt to guess the (n + 1)-st odd prime, but this will give almost always incorrect results, which can be prime or composite, and positive or negative. The absolute value of the first negative prime obtained in this way is equal to 281,581.[2]

1,000,003 is the smallest prime number larger than 1,000,000; and, as such, the smallest Class 2 number to be prime.

The number 4,432,676,798,593 is one of only four known Mersenne–Fermat primes, which are neither Fermat nor Mersenne primes.

9,007,199,254,740,881 is a positive integer equal to \(2^{53} - 111\). It is notable in computer science for being the largest prime number which can be represented exactly in the double floating-point format (which has a 53-bit significand).

10100+267 is the first prime after a googol. This number has been named as "gooprol".

The number \(\frac{10^{1,031}-1}{9}\) is the the largest known base 10 repunit prime.